Properties

 Label 380.2.v Level $380$ Weight $2$ Character orbit 380.v Rep. character $\chi_{380}(7,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $224$ Newform subspaces $3$ Sturm bound $120$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.v (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$380$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$3$$ Sturm bound: $$120$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(380, [\chi])$$.

Total New Old
Modular forms 256 256 0
Cusp forms 224 224 0
Eisenstein series 32 32 0

Trace form

 $$224 q - 2 q^{2} - 4 q^{5} - 20 q^{8} + O(q^{10})$$ $$224 q - 2 q^{2} - 4 q^{5} - 20 q^{8} - 2 q^{10} + 4 q^{12} - 4 q^{13} - 4 q^{17} - 64 q^{20} - 8 q^{21} + 22 q^{22} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 12 q^{30} - 12 q^{32} + 8 q^{33} - 68 q^{36} - 16 q^{37} - 30 q^{38} + 8 q^{40} - 16 q^{41} + 30 q^{42} - 56 q^{45} + 24 q^{46} - 28 q^{48} + 12 q^{50} - 18 q^{52} - 4 q^{53} - 16 q^{56} - 12 q^{57} - 140 q^{58} + 14 q^{60} - 72 q^{61} + 12 q^{62} - 48 q^{65} - 12 q^{66} + 4 q^{68} - 82 q^{70} + 56 q^{72} - 4 q^{73} + 60 q^{76} + 48 q^{77} + 48 q^{78} - 2 q^{80} + 40 q^{81} + 16 q^{82} + 20 q^{85} + 64 q^{86} + 104 q^{88} - 92 q^{90} + 4 q^{92} - 24 q^{93} - 32 q^{96} - 4 q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(380, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.v.a $4$ $3.034$ $$\Q(\zeta_{12})$$ None $$-4$$ $$6$$ $$-2$$ $$0$$ $$q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
380.2.v.b $4$ $3.034$ $$\Q(\zeta_{12})$$ None $$2$$ $$-6$$ $$-2$$ $$0$$ $$q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+\zeta_{12}+\cdots)q^{3}+\cdots$$
380.2.v.c $216$ $3.034$ None $$0$$ $$0$$ $$0$$ $$0$$